Earlier works on consensus consistency do not consider representation learning and use the knowledge reuse framework (see [1]},[2]}) where the cluster partitions are available (features are irrelevant) or the features of the data are fixed. For example, Fern and Brodley [3]}, successfully applied Random Projections to Consensus Clustering, by performing k-means clustering on multiple random projections of the fixed features of input data.
In contrast, the notion of consensus consistency here deals with learning representations that achieve a consensus on the cluster assignments of multiple clustering algorithms.
One example of methods that enforce consensus consistency is Local Aggregation (LA) [4]}. LA builds on ID task [5]} and proposes a method based on a robust clustering objective (using multiple runs of k-means) to move statistically similar data points closer in the representation space and dissimilar data points further away. However, Zhuang et al. [4]} does not evaluate for clustering metrics and only focuses on linear evaluation using the learned features. Subsequently, we conducted a study to evaluate the clustering performance of these features (see Appendix) and observe that LA performs poorly when evaluated for clustering accuracy.
In Definition REF , we inherently assume that the clustering algorithms under considerations have been tuned properly.
Unfortunately, the definition of consensus consistency is ill-posed, there can be arbitrarily many different partitions which can satisfy the given conditiona) Degenerate solution where all clusters assignments are the same, b) Random assignment can satisfy this condition given that all clustering are producing the same but random assignments. We show that when exemplar consistency used as an inductive bias the resulting objective function shows impressive performance on challenging data sets. Combining exemplar and population constraints with consensus consistency seamlessly and effectively for clustering is the basis of our proposed method.
